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Physical Review A

Narrow dip inside a natural linewidth absorption profile in a system of two atoms

Alexander A. Makarov

Published Nov 17, 2015• 5 citations
Publisher

Abstract

Absorption spectrum of a system of two closely spaced identical atoms displays, at certain preparation, a dip that can be much narrower than the natural linewidth. This preparation includes (i) application of a strong magnetic field at an angle $\ensuremath{\alpha}$, that is very close to the magic angle ${\ensuremath{\alpha}}_{0}=arccos(1/\sqrt{3})\ensuremath{\approx}{54.7}^{\ensuremath{\circ}}$, with respect to the direction from one atom to another, and (ii) in-plane illumination by a laser light in the form of a nonresonant standing wave polarized at the same angle $\ensuremath{\alpha}$. Both qualitative and quantitative arguments for the narrow dip effect are presented.

DOI
10.1103/physreva.92.053840

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Absorption spectrum of a system of two closely spaced identical atoms displays, at certain preparation, a dip that can be much narrower than the natural linewidth. This preparation includes (i) application of a strong magnetic field at an angle \ensuremathα\ensuremath{\alpha}\ensuremathα, that is very close to the magic angle \ensuremathα0=arccos(1/3)\ensuremath≈54.7\ensuremath∘{\ensuremath{\alpha}}_{0}=arccos(1/\sqrt{3})\ensuremath{\approx}{54.7}^{\ensuremath{\circ}}\ensuremathα0​=arccos(1/3​)\ensuremath≈54.7\ensuremath∘, with respect to the direction from one atom to another, and (ii) in-plane illumination by a laser light in the form of a nonresonant standing wave polarized at the same angle \ensuremathα\ensuremath{\alpha}\ensuremathα. Both qualitative and quantitative arguments for the narrow dip effect are presented.
Previous theoretical results on the influence of a laser on the line shape of a coupled transition-laser-induced line narrowing-have been restricted to the case where the laser is detuned from the center of its atomic gain profile or is in the form of a traveling wave. This paper extends those results to include the case where the laser is an intense standing-wave field tunable to the center of its atomic gain profile (conditions for Lamb dip). The effect may be observed either in transmission, by probing the coupled transition with a weak traveling-wave field coaxial with the laser field, or else in spontaneous emission from the coupled transition viewed along the axis of the laser field. It is now well known that for a laser detuned from the center of its atomic gain profile, two narrow Lorentzian resonances of different widths appear superimposed upon the broad background signal at frequencies symmetrically located about the corresponding line center. When the laser is tuned to the center of its gain profile, however, additional fine structure develops. This structure, which is particularly significant when the laser field is intense, may have important applications in highresolution spectroscopy and laser-frequency stabilization. In this paper the laser frequency may be smaller or larger than the frequency of the coupled transition. In the latter case an intense laser introduces additional splitting effects, even when the laser is detuned. Splitting effects due to weakly saturating laser fields are also discussed. The problem is formulated by expanding elements of the ensemble-averaged density matrix in an infinite series of spatial Fourier components. A perturbation technique is employed, valid for a weak probe field and a standing-wave field of arbitrary intensity. One obtains an expression for emission induced by the probe field due to atoms moving with one velocity, written in terms of continued fractions in the general case and with Bessel functions in an important special case. This expression is integrated over the atomic velocity distribution by means of a computer to obtain the total emission due to atoms moving with all velocities. In some cases the integrated expressions may be written in closed algebraic form. A detailed discussions of line shapes and of the physical processes involved is included.
We have investigated both theoretically and experimentally saturated absorption of a long-lifetime transition in a calcium atomic beam excited either by a standing wave or by two counterpropagating traveling waves. For standing-wave excitation the usual saturation dip is turned into a peak and then evolves into a triplet as the laser intensity is increased. A theoretical framework has been developed to account for the interaction of atoms with multiple-wave excitation based on a combination of free propagators and S matrices, also applicable to atomic interferometry. The shapes of the wave packets prepared by optical beam splitters are derived. The experimental size and shape of the absorption signal are reproduced by theory only when the actual laser profile is accurately represented and if the recoil physics is introduced because of multiple momentum exchanges between atoms and light in strong laser fields.
Resonance fluorescence of two two-level atoms driven by a coherent laser field propagating parallel to the interatomic axis is examined, taking into account the dipole-dipole interaction. We show that the number of peaks in the fluorescence intensity depends on the direction of observation with respect to the interatomic axis and on whether the system is driven by a standing-wave or a running-wave laser field. When the system is driven by the standing-wave field the fluorescence intensity shows two peaks and a dip for an observation direction perpendicular to the interatomic axis and three peaks in the direction parallel to it. When the system is driven by the running-wave field only two peaks are observed for the perpendicular direction. We explain these features in terms of the collective states of the system and show that the directional effect can be attributed to the fact that the antisymmetric state of the system does not radiate in the direction perpendicular to the interatomic axis. Photon statistics also demonstrate the directional effect for the standing-wave field. Frequency regimes are found where sub-Poissonian photon statistics occur. Depending on the direction of the observation, a state close to a Fock state can occur for one or two frequencies of the driving field, corresponding to zero-photon-number fluctuations or maximum sub-Poissonian behavior. The fluorescence spectrum is found to depend on the direction of observation and the interatomic separation. For small interatomic separations and a standing-wave driving field the spectrum exhibits seven lines for the perpendicular direction and 13 lines in the direction parallel to the interatomic axis. For the running-wave field the spectrum shows 13 lines independent of the direction of observation. Moreover, we show that for particular interatomic separations dark regimes appear in the spectrum. We discuss the effect of the dipole-dipole interaction on the dark states and explain the spectral features in terms of the dressed-atom model. We also consider the absorption spectrum of a weak probe beam illuminating the two-atom system. We show that apart from a weak dispersion structure, the spectrum shows large peaks as one of the atoms is moved to successive nodes of the field.